ISTANBUL—Turkey downed a Syrian warplane on Sunday for breaching its airspace, escalating tensions along the border as Prime Minister Recep Tayyip Erdogan pledged to take a tougher stance against President Bashar al-Assad a week before Turkish elections.

Shortly after lunchtime, a Turkish F-16 downed a Syrian MIG-23 with a missile after it failed to heed four warnings to reverse course and cruised slightly inside Turkish airspace,...